Schrödinger equation in the drift theory of cold plasma

Abstract

A two-dimensional flow of an ideal neutral plasma across a magnetic field B is considered. The magnetic field is frozen in the plasma and is proportional to the plasma density n: B∝n. All ions are assumed to have the same magnetic moment μ and, correspondingly, mechanical moment l. It is shown that the magnetic moment is doubled due to the drift motion. The equations of plasma hydrodynamics, to which terms proportional to l² have been added, are investigated within the framework of drift theory. The forces are due to the additional pressure of the drift velocity and are proportional to the Bohm potential$V_q \propto - (\Delta \sqrt n /\sqrt n )$. The equations derived by the Madelung transformation (transition to the Ψ function:$V_q \propto - (\Delta \sqrt n /\sqrt n )$) are reduced to the Schrödinger cubic equation, which yields a new type of dynamics. It is shown that solitons, or nonspreading wave packets, which correspond to magnetosound waves in linear theory, and steady states can occur in the plasma described.